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Applying directional antennas in wireless ad hoc networks can theoretically achieve higher spatial multiplexing gain and, thus, higher network throughput. However, in practice, deafness, hidden-terminal, and exposed terminal problems are exaggerated with directional antennas, and they cause the degradation of the overall network performance. Although there are several random-access-based medium-access control (MAC) protocols being proposed in the literature for networks with directional antennas, the deafness, hidden-terminal, and exposed terminal problems have yet to be fully solved. In this paper, we present a new MAC protocol called the dual-sensing directional MAC (DSDMAC) protocol for wireless ad hoc networks with directional antennas. Different from existing protocols, the DSDMAC protocol relies on the dual-sensing strategy to identify deafness, resolve the hidden-terminal problem, and avoid unnecessary blocking. The integrity of the DSDMAC protocol is verified and validated using , which is a formal protocol verification and validation tool. We further develop an analytical framework to quantify the performance of the DSDMAC protocol and conduct extensive simulations, which verify the accuracy of the analysis. The protocol verification, analysis, and simulation results show the robustness and superior performance of the DSDMAC protocol, which can achieve a much higher network throughput and lower delay utilizing the spatial multiplexing gain of the directional antennas. The results presented in this paper show that the proposed DSDMAC protocol can substantially outperform the state-of-the-art protocols.